The inverse of g(x) given by g(x) = x + 47, is g⁻¹(x) = x - 47, resulting in g⁻¹(0) = -47. For the function h represented by pairs, the value of h²¹(5) is -7.
The student has presented a question involving two one-to-one functions g and h. The function g(x) appears to be incorrectly represented, but assuming it is meant to be g(x) = x + 47, we can find g⁻¹(x) which is the inverse of g.
The inverse g⁻¹(x) is easily found by solving the equation y = x + 47 for x, leading to g⁻¹(x) = x - 47. Setting this to zero gives us g⁻¹(0) = 0 - 47 = -47.
The function h appears to be given as a set of ordered pairs. To find h²¹(5), we need to find the pair where the second element is 5, which is (-7, 5). Since h is one-to-one, its inverse function h²¹ will return the first element of the ordered pair, which is -7.