Question

5
select the correct answer.
consider the function.

x	-1	0	1	2
f(x)	-2	3	8	13

which function could be the inverse of function f?
a. | x | -1 | 0 | 1 | 2 |

p(x)

2

-3

-8

-13

b. | x | 1 | 0 | -1 | -2 |

s(x)

-2

3

8

13

c. | x | 2 | -3 | -8 | -13 |

r(x)

1

0

-1

-2

d. | x | -2 | 3 | 8 | 13 |

q(x)

-1

0

1

2

Explanation:

Step1: Recall inverse function rule

The inverse of a function swaps the input ($x$-values) and output ($f(x)$-values) of the original function. For the original function $f$, if $(a,b)$ is a point on $f$, then $(b,a)$ must be a point on $f^{-1}$.

Step2: List original function points

Original function $f$ has points: $(-1,-2), (0,3), (1,8), (2,13)$

Step3: Swap x and y for inverse

Swapping coordinates gives inverse points: $(-2,-1), (3,0), (8,1), (13,2)$

Step4: Match to options

Compare these points to the options: Option D has $x$-values $-2,3,8,13$ and $q(x)$-values $-1,0,1,2$, which matches the swapped points.

Answer:

D.

x	-2	3	8	13