Consider the functions f(x) = 2x + 1 and g(x) = x² - 10. What is the value of f[g(3)]?
39, -3, -7, -1

Solution:

g(x) = y\(_1\) = x² − 10 ….. (1)

f(x) = y\(_2\) = 2x + 1 ….. (2)

f(g(x)) is a composite function that can be written as (fog)(x)

Where x is present in f(x) you should substitute y\(_1\)

I.e., substituting equation (1) in x which is present in equation (2)

f(g(x)) = 2 y\(_1\) + 1 where y\(_1\) = x² − 10

f(g(x)) = 2 (x² − 10) + 1

f(g(x)) = 2x² - 20 + 1

f(g(x)) = 2x² - 19

Now substitute x = 3 in f [g(x)]

f[g(3)] = 2(3)² - 19

So we get

f[g(x)] = 18 - 19 = - 1

Therefore, f[g(x)] when x = 3 is - 1.

Consider the functions f(x) = 2x + 1 and g(x) = x² - 10. What is the value of f[g(3)]?
39, -3, -7, -1

Summary:

Consider the functions f(x) = 2x + 1 and g(x) = x² − 10. The value of f[g(3)] is - 1.