Question

how to solve this sum if f(x) = 2x-1/5x-2;x is not equal to 5/2. show that (f○f)(x)=x​

Answer 1

Answer:

3(x+1)

Step-by-step explanation:

(fog)(x)=f(g(x))=2(3x+2)−1=6x+4−1=6x+3=3(2x+1)

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Answer 2

Answer:

IF f(x) = $\frac{2x-1}{5x-2}$; x≠ $\frac{5}{2}$  then f(f(x)) = x

Step-by-step explanation:

Let,

F(x) = ax

Then F(f(x)) mean is we need to replace x by f(x)

f(f(x)) = a(f(x))

f(f(x)) = a(ax)

f(f(x)) =  $a^{2} x$

Now,

In question we have,

f(x) = $\frac{2x-1}{5x-2}$

f(f(x)) = $\frac{2f(x)-1}{5f(x)-2}$

f(f(x)) = $\frac{2\frac{2x-1}{5x-2} -1}{5\frac{2x-1}{5x-2}-2}$

f(f(x)) = $\frac{4x-2-5x+2}{10x-5-10x+4}$

f(f(x)) = $\frac{-x}{-1}$

f(f(x)) = x

Hence proved