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