Answer:
[tex]f(x)^{-1}[/tex] = 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4
Step-by-step explanation:
Given the function f(x), if f(x) ≠ 0, we would have the formula as following:
+) [tex]f(x)^{-1}[/tex] = 1/f(x)
We have the given equation:
f(x) = (10x/2) + 7 = 5x + 7
f(x) ≠ 0 when and only when (5x + 7) ≠ 0
(5x + 7) ≠ 0
⇔ 5x ≠ 0 - 7
⇔ 5x ≠ -7
⇔ x ≠ -7 ÷ 5
⇔ x ≠ -1.4
So with x≠ -1.4, f(x) ≠ 0, we have:
[tex]f(x)^{-1}[/tex] = 1/f(x) = 1/ (5x + 7)
Conclusion: [tex]f(x)^{-1}[/tex] = 1/(5x+7) [ 1 over (5x + 7)] with x≠ -1.4
