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Step-by-step explanation:
(f o g)(x)
= f(x² - 5)
= 4(x² - 5) + 1
= 4x² - 19.
Therefore (f o g)(4) = 4(4)² - 19 = 64 - 19 = 45.
Answer:
[tex]\boxed {\boxed {\sf 45}}[/tex]
Step-by-step explanation:
When solving a composition of function composition, work from the inside to the outside.
We have the composition:
We must start on the inside, and find g(4) first.
1. g(4)
The function for g is:
[tex]g(x)=x^2-5[/tex]
Since we want to find g(4), we have to substitute 4 in for x.
[tex]g(4)=(4)^2-5[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction. First we should solve the exponent.
[tex]g(4)=16-5[/tex]
Subtract 5 from 16.
[tex]g(4)= 11[/tex]
Now, since g(4) equals 11, we have:
2. f(11)
The function for f is:
[tex]f(x)= 4x+1[/tex]
We want to find f(11), so substitute 11 in for x.
[tex]f(11)= 4(11)+1[/tex]
Solve according to PEMDAS and multiply first.
[tex]f(11)= 44+1[/tex]
Add.
[tex]f(11)= 45[/tex]
(f o g)(4) is equal to 45.