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# Given that g(h(x)) = 2x^2 + 3x, and h(g(x)) = x^2 + 4x - 4 for all the

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Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Given that g(h(x)) = 2x^2 + 3x, and h(g(x)) = x^2 + 4x - 4 for all the  [#permalink]

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Updated on: 10 Aug 2019, 16:50
12
00:00

Difficulty:

95% (hard)

Question Stats:

24% (02:31) correct 76% (02:09) wrong based on 29 sessions

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Given that $$g(h(x))= 2x^2+3x$$, and $$h(g(x))=x^2+4x-4$$ for all the real values of x. Which of the following could be the value of g(-4)?

A. -3
B. -2
C. -1
D. 1
E. 2

Originally posted by nick1816 on 09 Aug 2019, 19:06.
Last edited by nick1816 on 10 Aug 2019, 16:50, edited 2 times in total.
Director
Joined: 19 Oct 2018
Posts: 880
Location: India
Re: Given that g(h(x)) = 2x^2 + 3x, and h(g(x)) = x^2 + 4x - 4 for all the  [#permalink]

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10 Aug 2019, 23:04
At x= -4, $$x^2+4x-4$$= -4 or x

$$g(h(x))= 2x^2+3x$$
Put x= g(x)

$$g(h(g(x)))= 2[g(x)]^2+3[g(x)]$$

$$g(x^2+4x-4)= 2[g(x)]^2+3[g(x)]$$

put x=-4

$$g(-4)= 2[g(-4)]^2+3[g(-4)]$$

$$2[g(-4)]^2+2[g(-4)] = 0$$

g(-4)= 0 or -1

C

nick1816 wrote:
Given that $$g(h(x))= 2x^2+3x$$, and $$h(g(x))=x^2+4x-4$$ for all the real values of x. Which of the following could be the value of g(-4)?

A. -3
B. -2
C. -1
D. 1
E. 2
Re: Given that g(h(x)) = 2x^2 + 3x, and h(g(x)) = x^2 + 4x - 4 for all the   [#permalink] 10 Aug 2019, 23:04
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