Question

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Answer 1

`f(-4) = 64`

Explanation:

Given

`(x_1,y_1) = (1,2)`

`(x_2,y_2) = (2,1)`

Required

Find f(-4)

We have that:

`y = ab^x`

For
`(x_1,y_1) = (1,2)`

`2 = ab^1`

`2 = ab`

For
`(x_2,y_2) = (2,1)`

`1 = ab^2`

Rewrite as:

`1 = ab * b`

Make b the subject

`b = (1)/(ab)`

Substitute:
`2 = ab`

`b = (1)/(2)`

Substitute
`b = (1)/(2)` in
`2 = ab`

`2 = a * (1)/(2)`

`a = 2 * 2`

`a = 4`

To calculate f(-4), we have:

`f(x) = ab^x`

`f(-4) = 4 * (1)/(2)^((-4))`

`f(-4) = 4 * 16`

`f(-4) = 64`