# If f(x) = 3x + 2 and g(x) = x^{2} + 1 which expression is equivalent to (f*g)(x)

(3x + 2)(x^{2} + 1)

3x^{2} + 1 + 2

(3x + 2)^{2} + 1

3(x^{2} + 1) + 2

**Solution:**

Given, the functions are

f(x) = 3x + 2

g(x) = x^{2} + 1

We have to find (f*g)(x)

This is a composite function, where f(x) takes the output values of g(x) as its inputs.

(f*g)(x) = f(g(x))

f(g(x)) = f(x^{2 }+ 1)

= 3(x^{2} + 1) + 2

Therefore, (f*g)(x) = 3(x^{2 }+ 1) + 2.

## If f(x) = 3x + 2 and g(x) = x^{2} + 1 which expression is equivalent to (f*g)(x)

**Summary:**

If f(x) = 3x + 2 and g(x) = x^{2} + 1, the expression equivalent to (f*g)(x) is 3(x^{2 }+ 1) + 2.

**Example:**

If f(x) = 2x + 2 and g(x) = x + 1 which expression is equivalent to (f*g)(x).

**Solution:**

Given, the functions are

f(x) = 2x + 2

g(x) = x + 1

We have to find (f*g)(x)

(f*g)(x) = f(g(x))

f(g(x)) = f(x + 1)

= 2(x + 1) + 2

= 2x + 2 + 2

= 2x + 4

Therefore, (f*g)(x) = 2x + 4.

**Summary:**

If f(x) = 2x + 2 and g(x) = x + 1, the expression equivalent to (f*g)(x) is 2x + 4.