Find fog(x),if f(x)=x+3÷4x-5 and g(x)=3+5x÷4x-1
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2 Answers

f(x)=(x+3)/(4x-5), g(x)=(3+5x)/(4x-1).

f o g(x)=f(g(x))=(g(x)+3)/(4g(x)-5)=

((3+5x)/(4x-1)+3)/(4(3+5x)/(4x-1)-5).

Multiply top and bottom by 4x-1:

(3+5x+12x-3)/(12+20x-20x+5)=17x/17=x.
by Top Rated User (736k points)

Find fog(x),if f(x)=x+3÷4x-5 and g(x)=3+5x÷4x-1

fog(x) = f(g(x)) = (g + 3/(4g - 5)

fog = ({3 + 5x}/{4x - 1} + 3)/(4{3 + 5x}/{4x - 1} - 5)

fog = ({3 + 5x} + 3{4x - 1})/(4{3 + 5x} - 5{4x - 1})

fog = {3 + 5x + 12x -3}/{12 + 20x -20x + 5}

fog = 17x/17

fog(x) = x

by Level 11 User (81.5k points)

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