Question

100 POINTS, WILL MARK BRAINLIEST! If h(x) = f[f(x)] use the table of values for f and f ′ to find the value of h ′(1).
Fill in the blank answer

Answer 1

Answer:

The value of $h^\prime(1)=5$

Step-by-step explanation:

Given that  $h(x)=f(f(x))$

now to find $h(x)=f(f(x))$ from the given functions f(x) and f'x

let $h(x)=f(f(x))$

Then put x=1 in above function we get

$h(1)=f(f(1))$

$=f(3)$ (from the table f(1)=3 and f(3)=6)

Therefore h(1)=6

Now to find h'(1)

Let

$h^{\prime}(x)=f^{\prime}(f^\prime(x))$ (since  $h(x)=f(f(x))$ )

put x=1 in above function we get

$h^{\prime}(1)=f^{\prime}(f^\prime(1))$

$=f^{\prime}(2)$    (From the table $f^\prime(1)=2$ and $f^\prime(2)=5$)

$h^{\prime}(1)=5$

Therefore $h^{\prime}(1)=5$

Answer 2

Answer:

h'(1) = 5

Step-by-step explanation:

So, we know that h(x) = f[f(x)].

We can use what we are given for f(x) and f'(x) to solve.

If we use x = 1,  we can substitute.

h(1) = f[f(1)]

Looking at the table, we know that f(3) = 6, f(2) = 1, and f(1) = 3.

Now solve for h'(1). Note that x = 1.

h'(1) = f[f(1)]

Using the table we know that f'(1) = 2 and f'(2) = 5.

So, h'(1) = 5

Best of Luck!