Question

Use Desmos to match each pair of functions to the right description: are they inverses or not? Check if f(g(x)) =g(f(x)) =x. The functions are f(x)=x^2+1 and g(x)=x-1, f(x)=7x and g(x)=x/7. Are they inverse functions or not inverse functions.

Answer 1

Compute the compositions.

Pair A: f(x) = x^2 + 1, g(x) = x − 1
- f(g(x)) = (x − 1)^2 + 1 = x^2 − 2x + 2 (not equal to x in general)
- g(f(x)) = (x^2 + 1) − 1 = x^2 (not equal to x in general)
Conclusion: NOT inverses.

Pair B: f(x) = 7x, g(x) = x/7
- f(g(x)) = 7*(x/7) = x
- g(f(x)) = (7x)/7 = x
Conclusion: They ARE inverse functions (for all real x).