Question

Which functions are the same as their inverse functions?

f(x) = 175, -5
g(x) = 5-1, 11
h(x) = 1
k(x) = 5-2, 172
a) f(x)
b) g(x)
c) h(x)
d) k(x)

Answer 1

The function that is the same as its inverse among the given options is h(x) = 1, because it is a horizontal line which is unchanged when reflected over the line y = x.

Step-by-step explanation:

The question is asking which functions are the same as their inverse functions. To find the function that is its inverse, we look for a function where f(x) = f-1(x). Functions that are their inverses typically reflect over the line y = x. Common examples of such functions are the identity function, f(x) = x, the reciprocal function, f(x) = 1/x for x not equal to 0, and certain constant functions.

Given the options:

• f(x) = 175
• g(x) = 5-1
• h(x) = 1
• k(x) = 5-2

we can see that h(x) = 1 is the function that is the same as its inverse, as the graph of y = 1 is a horizontal line that remains unchanged when reflected over the line y = x.