If f(x) = 2x – 1 and g(x) = x^2 – 2, find [g · f](x) please show me how to do this

Question

If f(x) = 2x – 1 and g(x) = x^2 – 2, find [g · f](x)

please show me how to do this

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Claire 2 weeks 2021-09-13T13:44:21+00:00 2 Answers 0

Answers ( )

    0
    2021-09-13T13:45:21+00:00

    Answer:

    (x² -7)/(2x + 1)

    Step-by-step explanation:

    f(x) = 2x+1 and g(x) = x² -7

    thus: (g/f)(x) = g(x)/f(x) = x² -7/2x + 1

    0
    2021-09-13T13:46:05+00:00

    Hello!

    The answer is:

    (g \circ f)(x)=4x^{2}-4x-1

    Why?

    To solve the problem, we need to remember that composing functions means evaluate a function into another different function.

    Also, we need to remember how to solve the following notable product:

    (a-b)^{2}=a^{2}-2ab+b^{2}

    We have that:

    (g \circ f)(x)=g(f(x))

    Now, we are given the equations:

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

    So, composing we have:

    (g \circ f)(x)=g(f(x))

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

    Now, we have to solve the notable product:

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

    (g \circ f)(x)=4x^{2}-4x+1-2

    Hence, we have that:

    (g \circ f)(x)=4x^{2}-4x-1

    Have a nice day!

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