1.

Find f(x)g (x) = x² + x - 2 and (gof) (x) = 4x² -10x + 4​

Answer»

Answer:

2x-3

Step-by-step explanation:

given G(x)=x²+x-2

and gof(x)=4x²-10x+4=>g(F(x))=4x²-10x+4...(1)

g(f(x)) is ALSO equal to f(x)²+f(x)-2...(2)

from 1 and 2 we get

f(x)²+f(x)-2=4x²-10x+4

f(x)²-f(x)+2F(x)-2=4x²-8x-2x+4

f(x)²+f(x)+(1/2)²=4x²-10x+4+2+(1/2)²

(f(x)+1/2)²=4x²-10x+6+1/4

(f(x)+1/2)²=4x²-10x+25/4=(2x-5/2)²

f(x)+1/2=2x-5/2

f(x)=2x-3



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