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it's not a really a question but how to solve these types of questions

Let f(x) = 9x − 2 and g(x) = −x + 3. Find f(g(x)).


Let f(x) = 2x + 2. Solve f−1(x) when x = 4.


Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).


Let f(x) = x2 − 8x + 5. Find f(−1).

Verified Answer :

  1. 9(-x+3) - 2
    3.[ (2)2 - 6(2) - 7] + 8
    4.(-1)2 - 8(-1) + 5

Answer:

Part 1) \(f(x) = 9x- 2\)  and \(g(x) = -x + 3\)

Find f(g(x)).

\(f(x) = 9x- 2\)

Substitute value of g(x) in place of x

\(f(g(x)) = 9(-x+3)- 2\)

\(f(g(x)) = -9x+27- 2\)

\(f(g(x)) = -9x+25\)

So, \(f(g(x)) = -9x+25\)

Part 2) \(f(x) = 2x + 2\)

\(y = 2x + 2\)

Replace y with x and x with y

\(x = 2y + 2\)

Find y

\(\frac{x-2}{2} = y\)

So, \(f^{-1}(x)=\frac{x-2}{2}\)

Substitute x = 4

\(f^{-1}(4)=\frac{4-2}{2}\)

\(f^{-1}(4)=1\)

Part 3) \(f(x) = x + 8\) and \(g(x) = x^2- 6x-7\)

\(f(x) = x + 8\)

Substitute value of g(x) in place of x

\(f(g(x)) =x^2- 6x-7 + 8\)

\(f(g(x)) =x^2- 6x+1\)

Substitute x = 2

\(f(g(x)) =2^2- 6(2)+1\)

\(f(g(x)) =4- 12+1\)

\(f(g(x)) =-7\)

Part 4) \(f(x) = x^2-8x + 5\)

Substitute x = -1

\(f(-1) = (-1)^2-8(-1) + 5\)

\(f(-1) =14\)

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