Question

If f(x + 2) = 2x + 3 then find f-'(4).​

Answer 1

Given:

The function is

$f(x+2)=2x+3$

To find:

The value f'(4).

Solution:

We have,

$f(x+2)=2x+3$

Putting $x+2=t$ and $x=t-2$ we get

$f(t)=2(t-2)+3$

$f(t)=2t-4+3$

$f(t)=2t-1$

Differentiate with respect to t.

$f'(t)=2(1)-0$

$f'(t)=2$

At $t=4$, we get

$f'(4)=2$

Therefore, the value of f'(4) is 2.