Math Problem Statement

jawab dengan benar

Diketahui fungsi f(x) = 3x - 5 dan g(x) = (4x - 2) / (6 - 4x). Nilai komposisi fungsi (g o f)(2) adalah?

Solution

We are given two functions:

f(x)=3x5f(x) = 3x - 5 g(x)=4x264x,with x32g(x) = \frac{4x - 2}{6 - 4x}, \quad \text{with } x \neq \frac{3}{2}

We need to find the value of (gf)(2)(g \circ f)(2), which represents the composition of gg and ff evaluated at x=2x = 2.

Step 1: Find f(2)f(2)

First, we substitute x=2x = 2 into the function f(x)f(x):

f(2)=3(2)5=65=1f(2) = 3(2) - 5 = 6 - 5 = 1

Step 2: Find g(f(2))=g(1)g(f(2)) = g(1)

Now that we know f(2)=1f(2) = 1, we substitute this value into the function g(x)g(x):

g(1)=4(1)264(1)=4264=22=1g(1) = \frac{4(1) - 2}{6 - 4(1)} = \frac{4 - 2}{6 - 4} = \frac{2}{2} = 1

Thus, the value of (gf)(2)(g \circ f)(2) is 11.

The correct answer is: d.1\boxed{d. 1}

Would you like further explanation or have any other questions?

Related Questions:

  1. What is the domain of the composite function gfg \circ f?
  2. If f(x)=2x4f(x) = 2x - 4, how would the composite function change?
  3. What happens if x=32x = \frac{3}{2}? Why is it excluded?
  4. Can we always compose two functions, or are there restrictions?
  5. How can the composition of functions be applied to real-world problems?

Tip:

When evaluating composite functions, always work from the inside out, starting with the innermost function.

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Math Problem Analysis

Mathematical Concepts

Function Composition
Algebra

Formulas

f(x) = 3x - 5
g(x) = (4x - 2) / (6 - 4x)
Function composition: (g o f)(x) = g(f(x))

Theorems

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Suitable Grade Level

Grades 10-12