Answer:
x : 2,4,6,8
f(x) :12,6,4,3
This table represents the relationship of an inverse variation.
Explanation:
We are asked to find which relationship shows an inverse variation.
Inverse variation means that there exist a constant 'k' such that:
f(x)=k/x
or, k=x·f(x)
1)
x : 2, 3, 4, 5
f(x): 1, 4, 9, 16
if x=2 and f(x)=1
k=2
but if x=3 and f(x)=4
we get: k=12.
Hence, we do not obtain a same constant k.
2)
x: 1,2,3,4
f(x):2,8,18,32
when x=1 , f(x)=2
⇒ k=2
when x=2 , f(x)=8
⇒ k=16
Hence, we did not get a same constant 'k'.
3)
x: 1,2,3,4
f(x):4,3,2,1
when x=1, f(x)=4
⇒ k=4
when x=2 , f(x)=3
⇒ k=6
Hence, we did not get a same constant 'k'.
4)
x :2,4,6,8
f(x) :12,6,4,3
when x=2 f(x)=12
⇒ k=2×12=24
when x=4 f(x)=6
⇒ k=4×6=24
when x=6 f(x)=4
⇒ k=6×4=24
when x=8 f(x)=3
⇒ k=8×3=24
Hence, we get a constant 'k=24' for all the values of x.
Hence, option: 4 shows relationship of an inverse variation.
x :2,4,6,8
f(x) :12,6,4,3