Question

Let f(x) = 5x - 1 and g(x) = x2 + 2.
Find (f o g)(3).

Answer 1

Considering the definition of composite function, (f o g)(3) is 54.

The composite function is one that is obtained through an operation called composition of functions, which consists of successively applying the functions that are part of the operation.

That is, the composition of functions consists of evaluating the same value of the independent variable (x) in two or more functions successively. For example, the composition of functions (f o g)(x) results in the composite function f[g(x)].

In this case, being f(x) = 5x - 1 and g(x) = x² + 2, the function (f o g)(x) is:

(f o g)(x)= f[g(x)]= 5×(x² + 2) -1

(f o g)(x)= 5x² + 5×2 -1

(f o g)(x)= 5x² + 10 -1

(f o g)(x)= 5x² + 9

Finally:

(f o g)(3)= 5×(3)² + 9

(f o g)(3)= 5×9 + 9

(f o g)(3)= 45 + 9

(f o g)(3)= 54

In summary, (f o g)(3) is 54.

Answer 2

( f ∘ g ) ( x ) = 10 x − 3

Explanation:

Just plug the formula for g ( x ) into the formula for f ( x ) (so replace x in the formula for f ( x ) with what g ( x ) equals), then simplify:

( f ∘ g ) ( x ) = f ( g ( x ) ) = f ( 2 x − 1 ) = 5 ( 2 x − 1 ) + 2 = 10 x − 5 + 2 = 10 x − 3 .