Question

PLZ HELP

given f(x)=x+1 and g(x) = x^2, what is (g∘f) (x)

(g ∘ f) (x) = (x+1)^2

(g ∘ f) (x) = x^2(x+1)

(g ∘ f) (x) = x^2+1

(g ∘ f) (x) = x^2+x+1

Answer 1

The composition (g \circ f)(x), where f(x) = x+1 and g(x) = x^2, is calculated by substituting f(x) into g(x), resulting in (x+1)^2, which expands to x^2 + 2x + 1.

Step-by-step explanation:

When considering the functions f(x) = x+1 and g(x) = x^2, the composition (g \circ f)(x) is obtained by plugging the function f into the function g. This means we first apply f to x, and then apply g to the result of f(x). Therefore, we have the following steps:

1. Compute f(x) which is x+1.
2. Substitute f(x) into g(x), which gives us g(f(x)) = g(x+1).
3. Since g(x) = x^2, then g(x+1) = (x+1)^2.
4. Finally, expand the binomial to get (x+1)^2 = x^2 + 2x + 2

Hence, (g \circ f)(x) = x^2 + 2x + 1.

Answer 2

B) (x+1) ( x²).

Step-by-step explanation:

Given : f(x)=x+1 and g(x) = x².

To find : what is (g∘f) (x).

Solution : We have given

f(x)=x+1 and g(x) = x².

By the rule :

(g∘f) (x) = g(x) * f(x).

Plugging the values

(g∘f) (x) = (x+1) ( x²).

Therefore, B) (x+1) ( x²).