Math Problem Statement

1. Diketahui f(x) = 5x - 6 a) g(x) jika (f o g)(x) = 5x + 9 b) g(-2) jika (g o f)(x) = 5x - 3 2. Diketahui f(x) = (x + 6) / (2x - 5) dan g(x) = 3x + 1 a) (g o f^{-1})(x) b) (g o f)^{-1}(x) 3. (Incomplete)

Solution

The image contains some mathematical questions that involve functions, compositions, and their inverses. Let's break them down:

  1. f(x)=5x6f(x) = 5x - 6

    a) Find g(x)g(x) if (fg)(x)=5x+9(f \circ g)(x) = 5x + 9.

    b) Find g(2)g(-2) if (gf)(x)=5x3(g \circ f)(x) = 5x - 3.

  2. f(x)=x+62x5f(x) = \frac{x + 6}{2x - 5} and g(x)=3x+1g(x) = 3x + 1.

    a) Find (gf1)(x)(g \circ f^{-1})(x).

    b) Find (gf)1(x)(g \circ f)^{-1}(x).

  3. The third question is incomplete, as only "dk" is written.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Inverse Functions
Function Composition

Formulas

f(x) = 5x - 6
f(x) = (x + 6) / (2x - 5)
g(x) = 3x + 1
Composition of Functions: (f o g)(x) = f(g(x))

Theorems

Inverse Function Theorem
Properties of Function Composition

Suitable Grade Level

Grades 10-12