Help me with my Other example. Here is a photo

High School
Other

Lester Ilao

Answered question

2022-08-27

Answer & Explanation

Mr Solver

Skilled2023-06-05Added 147 answers

To solve the given problem, we will find the composite functions:
a) To find

(f \cdot g) (x)

, we need to substitute

g (x)

into

f (x)

.
Substituting

g (x) = x + 1

into

f (x)

, we have:

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

Therefore,

(f \cdot g) (x) = x^{2} + 2 x

.
b) To find

(g \cdot f) (- 1)

, we need to substitute

- 1

into

f (x)

and then substitute the result into

g (x)

.
Substituting

f (x) = x^{2} - 1

into

g (x)

, we have:

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

Substituting

- 1

into

x^{2}

, we have:

(g \cdot f) (- 1) = (- 1)^{2} = 1

Therefore,

(g \cdot f) (- 1) = 1

.

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