Question

Graph the functions on the same coordinate plane.

Answer 1

Using the given functions, the solution to the equation f(x)=g(x) is x = 1, 4.

What is a function?

• A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
• In simple words, a function is a relationship between inputs where each input is related to exactly one output.
• Every function has a domain and codomain or range.
• A function is generally denoted by f(x) where x is the input.
• The general representation of a function is y = f(x).

We have:

• f(x)=x² - 4x + 5
• g(x) = x + 1

We need to calculate: f(x) = g(x)

Now, calculate as follows:

• x² - 4x + 5 = x + 1
• x² - 4x + 5 -x -1 =0
• x² - 5x + 4 = 0
• x² - 4x -x +4 = 0
• x (x-4) -1(x-4) = 0
• x =1, 4

Therefore, using the given functions, the solution to the equation f(x)=g(x) is x = 1, 4.

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