 Mathematics
functions and relations

### Question Description

I need an explanation for this Mathematics question to help me study.

1) Find f(g(x)) if f(x) = 3x + 1 and g(x) = x2 - 1.

2) Find g(f(x)) if f(x) = 2x – 3 and g(x) = x2 - 1.

3)Find the zeros of f(x) =

4) Find the zeros of f(x) = Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service. 1) Replace x= x^2 - 1 in f(x)

f(g(x)) = f(x^2 - 1) = 3 ((x^2)-1) + 1

= 3 x^2 -3 + 1  distributing 3 inside the parenthesis

= 3 x^2 - 2

2) Replace x= 2x-3 in g(x)

g(f(x) = g(2x-3) = (2x-3)^2 - 1

= (2x)^2 - 2(2x)(3) + 3^2 - 1       because (ax-b)^2 = a^2x^2 - 2 abx + b^2

= 4 x^2 - 12x + 9  - 1

= 4 x^2 - 12x + 8           you can divide by 4 to simplify

= x^2 - 3x + 2

3) Zeros of a function f(x) = 0 but you need to know the function.

Ex: f(x)  = 3x + 1 = 0

3x +1 -1 = 0 - 1

3x = -1     then dividing by 3 both sides

x= -1/3  is the zero of the function

Ex: f(x) = 2x - 3 = 0

2x - 3 + 3 = 0 + 3

2x = 3          then dividing by 2

x = 3/2  is the zero of the function. IleanaP (262)
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