Question

Given the functions f(x) = -x + 23 andg(x) = 2x - 7, find the value of x for whichf(x) = g(x).A: 5B: 10C: 16D: 30

Answer 1

f(x) = -x + 23

g(x) = 2x - 7

We need to find the value of x for which f(x) = g(x), therefore:

`\begin{gathered} -x+23=2x-7 \\ \text{Solving for x:} \\ \text{Add x to both sides:} \\ -x+23+x=2x-7+x \\ 23=3x-7 \\ \text{Add 7 to both sides:} \\ 23+7=3x-7+7 \\ 30=3x \\ \text{Divide both sides by 3:} \\ (30)/(3)=(3x)/(3) \\ 10=x \end{gathered}`

Therefore, x = 10

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f(n) = n³ + 1

Where:

n ∈ Z ; n > 0

We need to find the first four terms, so:

f(1) = 1³ + 1 = 2

f(2) = 2³ + 1 = 8 + 1 = 9

f(3) = 3³ + 1 = 27 + 1 = 28

f(4) = 4³ + 1 = 64 + 1 = 65

Therefore, the first four terms are:

2 , 9 , 28 , 65