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3 years ago

8

If f(x) = square root of x+3, what is the equation for f–1(x)? f–1(x) = x2 - 3 f–1(x) = x2 + 3 f–1(x) = (x - 3) 2 f–1(x) = (x +

3) 2

1 answer:

cupoosta [38]3 years ago

3 0

Answer:

$\Large \boxed{\sf \ \ f^{-1}(x)=x^2-3 \ \ }$

Step-by-step explanation:

Hello,

$\text{For }x+3\geq 0\\\\f(x)=\sqrt{x+3}\\\\x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)+3}\\\\\text{*** take the square ***}\\\\f^{-1}(x)+3=x^2\\\\\text{*** subtract 3 from both sides ***}\\\\\large \boxed{\sf \ \ f^{-1}(x)=x^2-3 \ \ }\\$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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