Question

F:xn/2x+1 and g:x'n 50-1 find g-¹ and g-¹ of 3​

Answer 1

The inverse function of g, denoted as g⁻¹, is found by solving for y in the equation g(x) = 50 - x, leading to g⁻¹(x) = 50 - x. To find g⁻¹ of 3, we substitute x with 3, yielding g⁻¹(3) = 47.

Step-by-step explanation:

The student is asking how to find the inverse function of g, designated as g⁻¹, and then how to calculate g⁻¹ of 3. To find the inverse of g, we need to solve the equation g(x) = 50 - x for x.

1. Rewrite the function as y = 50 - x.
2. Swap x and y to find the inverse: x = 50 - y.
3. Solve for y to find g⁻¹(x): y = 50 - x, hence g⁻¹(x) = 50 - x.
4. Calculate g⁻¹(3) by substituting x with 3: g⁻¹(3) = 50 - 3 = 47.

Therefore, the inverse function g⁻¹(x) = 50 - x, and g⁻¹(3) = 47.