SOLUTION: For the real-valued function f(x) and g(x) bellow find (f o g)(5). f(x)=2^(x-3) and g(x)= square root of (x^2+39) The correct answer is one of the following. Which one is co

Algebra ->  Functions -> SOLUTION: For the real-valued function f(x) and g(x) bellow find (f o g)(5). f(x)=2^(x-3) and g(x)= square root of (x^2+39) The correct answer is one of the following. Which one is co      Log On


   

Question 1199001: For the real-valued function f(x) and g(x) bellow find (f o g)(5).

f(x)=2^(x-3) and g(x)= square root of (x^2+39)
The correct answer is one of the following. Which one is correct?
A) square root of 55
B) 32
C) 4
D) 8
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Mostly can be done using substitutions

f of g of x for x at 5.
Evaluate g(5). Use as input to evaluate f at g(5).

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The notation (f o g)(x) is the same as f( g(x) ).

To evaluate f( g(5) ), we first need the value of g(5).
g%28x%29+=+sqrt%28x%5E2%2B39%29

g%285%29+=+sqrt%285%5E2%2B39%29

g%285%29+=+sqrt%2825%2B39%29

g%285%29+=+sqrt%2864%29

g%285%29+=+8

This means,
f%28g%285%29%29+=+f%288%29

f%28x%29+=+2%5E%28x-3%29

f%288%29+=+2%5E%288-3%29

f%288%29+=+2%5E%285%29

f%288%29+=+highlight%2832%29
and furthermore,
f%28g%285%29%29+=+%28f+o+g%29%285%29+=+highlight%2832%29