Let f(x)=2xt2. Solve f^-1 (x) when x=4
1 answer:
Replace <span /><span>fx" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span>f</span></span><span><span><span>(</span></span><span><span>x</span></span><span><span>)</span></span></span></span></span></span></span></span><span>fx</span></span> with <span /><span>y" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span>y</span></span></span></span></span></span><span>y</span></span>.<span /><span>4⁢x-12" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span><span>4</span></span><span><span /></span><span><span>x</span></span></span><span><span><span>−</span></span><span><span>12</span></span></span></span></span></span></span></span><span>4x-12</span></span>Interchange the <span>variables</span>.<span /><span>x=4⁢y-12" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span>x</span></span><span><span>=</span></span><span><span><span><span>4</span></span><span><span /></span><span><span>y</span></span></span><span><span><span>−</span></span><span><span>12</span></span></span></span></span></span></span></span></span><span>x=4y-12</span></span>Solve for <span /><span>y" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span>y</span></span></span></span></span></span><span>y</span></span>.<span>Tap for more steps...</span><span /><span>y=3+x4" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span>y</span></span><span><span>=</span></span><span><span><span>3</span></span><span><span>+</span></span><span><span><span><span><span><span>x</span></span></span></span><span><span><span><span>4</span></span></span></span><span /></span><span /></span></span></span></span></span></span></span><span>y=3+x4</span></span>Solve for <span /><span>y" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span>y</span></span></span></span></span></span><span>y</span></span> and replace with <span /><span>f-1⁢x" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span><span><span>f</span></span></span><span><span><span><span>−</span></span><span><span>1</span></span></span></span></span><span><span /></span><span><span><span>(</span></span><span><span><span>x</span></span></span><span><span>)</span></span></span></span></span></span></span></span><span>f-1x</span></span>.<span>f-1⁢x=3+x4" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span><span><span><span><span><span><span><span><span><span>f</span></span></span><span><span><span><span>−</span></span><span><span>1</span></span></span></span></span><span><span /></span><span><span><span>(</span></span><span><span><span>x</span></span></span><span><span>)</span></span></span></span><span><span>=</span></span><span><span><span>3</span></span><span><span>+</span></span><span><span><span><span><span><span>x</span></span></span></span><span><span><span><span>4</span></span></span></span><span /></span><span /></span></span></span></span></span></span></span></span><span><span>f<span>−1</span></span><span>(x)</span></span>=<span>3+<span><span>x4
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