Question

If (x) =x+3/4x-5,g(x)=3+5x/4x-1,show that (f•g) x=x

Answer 1

Answer:

f(X)=(X+3)/(4x-5)

g(X)=(3+5x)/(4x-1)

then,

f.g(X)=f{g(X)}

=f{3+5x/4x-1}

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

={(3+5x+12x-3)/12+20x-20x+5}

= X (proved). .........

Answer 2

Answer withStep-by-step explanation:

Given:

$f(x)=\frac{x+3}{4x-5}$

$g(x)=\frac{3+5x}{4x-1}$

To show that $(f\cdot g)x=x$

LHS

$(f\cdot g)(x)=f(g(x))=f(\frac{3+5x}{4x-1})$

$(f\cdot g)(x)=\frac{\frac{3+5x}{4x-1}+3}{4(\frac{3+5x}{4x-1})-5}$

$(f\cdot g)(x)=\frac{(3+5x+12x-3)(4x-1)}{(4x-1)(12+20x-20x+5)}$

$(f\cdot g)(x)=\frac{17x}{17}=x$

LHS=RHS

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