Question

Evaluate inverse functions Find the following values f^-1(f(3.14)) F(f(-7))

Answer 1

Answer:

1. 3.14

Step-by-step explanation:

If we have

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

That just equals

$x$

For example, consider function

$f(x) = 2 {}^{x}$

The inverse of that function is

$y = 2 {}^{x}$

$x = 2 {}^{y}$

$log_{2}(x) = log_{2}(2 {}^{y} )$

$log_{2}(x) = y$

So

$f {}^{ - 1} (x) = log_{2}(x)$

If we compose the function, f(x) into f^-1(x).

We get

$log_{2}(2 {}^{x}) = x$

That proof of that.

1. Here x=f^-1(3.14)and f(3.14) cancel out so the answer is 3.14

2. We first find f(-7) which is -12,

We then find f(-12)= 5 so the answer here is 5.