Write the fractions as fractions with a common denominator 3/4 and 1/3

1 answer:

3 0

3/4 and 1/3

4x3 = 12 that will be the common denominator.

For 3/4 we first divide 12/4 = 3 and then multiply 3 x3 = 9 that's the numerator

For 1/3 we first divide 12/3 = 4 and then multiply 1x4 = 4 that's the numerator

The fractions will be rewrited as: 9/12 and 4/12

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seraphim [82]

Answer:

$y=\frac{x}{2}+\frac{2}{3}$

Step-by-step explanation:

The inverse function $f^{-1}$ of a function $f$ must meet that if $f(a)=b$ , then $f^{-1}(b)=a$ .
To find the inverse function one can clear out x from the initial equation, and once obtained an expression x=f(y), replace x by y, where y=f(x).
In this case, $y=h(x)=2x-\frac{4}{3}$ .
To find the inverse function, we clear out x, as follows: $y=2x-\frac{4}{3}$ ⇒ $y+\frac{4}{3} =2x$ ⇒ $x=\frac{y}{2}+\frac{2}{3}$ .
Now that we have clear out the value of x as a function of y, we just have to replace x by y: $y=\frac{x}{2}+\frac{2}{3}$ , which is the inverse function we have been looking for.

To corroborate the function is correct, we can use the fact that $f(a)=b$ , then $f^{-1}(b)=a$ . If we take x=1, in the first equation $f(1)=2-\frac{4}{3} = \frac{2}{3}$ . If now we replace b=2/3 in the inverse function we obtain $f^{-1}(\frac{2}{3})=\frac{\frac{2}{3} }{2} +\frac{2}{3} =1$