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Let f(x) =2x+1 and g(x)=x^2-1. Find the following

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(gof)(2x)
asked Nov 26, 2014 in ALGEBRA 2 by doan12345 Pupil
reshown Nov 26, 2014 by yamin_math

1 Answer

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The functions are f(x) = 2x + 1 and g(x) = x2 - 1

f(x) = 2x + 1

f(2x) = 2(2x) + 1

f(2x) = 4x + 1

 

(gof)(2x) = g(f(2x))

= g(4x + 1)

Now substitute this expression (4x + 1) in to function g in place of the x value.

= (4x + 1)2 - 1

= (4x)2 + (1)2 + 2(4x)(1) - 1

= 16x2 + 1 + 8x - 1

(gof)(2x) = 16x2 + 8x.

answered Nov 26, 2014 by david Expert

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