Question

Use f(x) = 2 x and f-'(x) = 2x to solve the problems.

Answer 1

Answer:

a) 1

b) 2

c) 2

Step-by-step explanation:

a) $f(2)$ means find the output for $\frac{1}{2}x$ when $x=2$.

$\frac{1}{2}(2)$

$\frac{2}{2}$

$1$

b) $f^{-1}(1)$ means find the output for $2x$ when $x=1$

$2(1)$

$2$

c) If $f$ and $f^{-1}$ are truly inverses then $f(f^{-1}(u))=u$ and $f^{-1}(f(u))=u$ as long as $u$ satisfies the domains.

So we should be able to conclude that $f^{-1}(f(2))=2$ with no work.

However, I will also show work.

$f^{-1}(f(2))$

$f^{-1}(1)$    since    $f(2)=1$ from part a.

$2$            since    $f^{-1}(1)=2$ from part b.