Math Problem Statement

𝑔(π‘₯) = 5π‘₯ βˆ’ 7 ; 𝑓𝑖𝑛𝑑 𝑔(π‘₯ 2 + 1)

Solution

To find g(x2+1)g(x^2 + 1) for the given function g(x)=5xβˆ’7g(x) = 5x - 7, we need to substitute x2+1x^2 + 1 into the function g(x)g(x).

The function g(x)g(x) is given as:

g(x)=5xβˆ’7g(x) = 5x - 7

Substitute x2+1x^2 + 1 for xx in the function:

g(x2+1)=5(x2+1)βˆ’7g(x^2 + 1) = 5(x^2 + 1) - 7

Now, distribute the 5:

g(x2+1)=5x2+5βˆ’7g(x^2 + 1) = 5x^2 + 5 - 7

Finally, simplify the expression:

g(x2+1)=5x2βˆ’2g(x^2 + 1) = 5x^2 - 2

So, g(x2+1)=5x2βˆ’2g(x^2 + 1) = 5x^2 - 2.

Would you like to explore this further or need more explanations?


Here are 8 related questions you might find useful:

  1. How do you evaluate functions at composite expressions like g(x2+1)g(x^2 + 1)?
  2. What is the general form of a linear function?
  3. How do you find the inverse of the function g(x)=5xβˆ’7g(x) = 5x - 7?
  4. What is the effect of substituting a quadratic expression into a linear function?
  5. How would you evaluate g(x2βˆ’1)g(x^2 - 1) for the same function g(x)=5xβˆ’7g(x) = 5x - 7?
  6. Can you graph the function g(x2+1)g(x^2 + 1)?
  7. How do you find the roots of g(x2+1)=0g(x^2 + 1) = 0?
  8. How do you determine the range of the function g(x2+1)g(x^2 + 1)?

Tip: When substituting expressions into functions, ensure each part is simplified correctly before combining like terms.

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Math Problem Analysis

Mathematical Concepts

Function evaluation
Linear functions
Substitution

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12