Math Problem Statement

The user submitted several math problems involving algebraic functions, function compositions, and inverse functions.

Solution

I see the photo you uploaded contains several math problems written on a whiteboard. Here's a transcription of the problems:

  1. Problem 6:
    Jika fg(x)=2x23f \circ g (x) = 2x^2 - 3 dan g(x)=3x+1g(x) = 3x + 1, maka tentukan f(x)f(x).

  2. Problem 7:
    Bahan baku sejumlah xx diubah menjadi barang jadi sejumlah f(x)=x12+4f(x) = \frac{x}{12} + 4. Barang jadi sejumlah yy akan dijual sehingga menghasilkan pendapatan y=200v320y = 200v - 320 dalam satuan ribu rupiah. Jika terdapat bahan baku sejumlah 144, maka pendapatan yang diperoleh adalah?

  3. Problem 8:
    Jika diketahui f(x)=x+32xf(x) = \frac{x+3}{2x}, maka f1(x)f^{-1}(x) adalah?

  4. Problem 9:
    Jika diketahui f(x)=2x+3x+5f(x) = \frac{2x + 3}{x + 5}; x5x \neq -5, dan g(x)=3x+1g(x) = 3x + 1, tentukan (fg)1(2)(f \circ g)^{-1}(2).

  5. Problem 10:
    Diketahui f(x)=2x+2x+1f(x) = \frac{2x+2}{x+1} dan g(0)=3g(0) = 3, serta g1(4)(6)=7g^{-1}(4)(6) = 7, maka nilai gg adalah?

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Function Composition
Inverse Functions

Formulas

f(x) ∘ g(x) = f(g(x))
Inverse Function: f^(-1)(x)
Linear functions

Theorems

Inverse function theorem
Function composition

Suitable Grade Level

Grades 10-12