Question

Inverse for h(x)=2x-4/3

Answer 1

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  $f^{-1}(\frac{2}{3})=\frac{\frac{2}{3} }{2} +\frac{2}{3} =1$