Question

Find a possible formula?

Answer 1

(a) `f(x) = 231/4 x + 121/2`

(b) `f(x) = 114^x`

(c) `f(x) = 11/4 x^6`

Explanation:

We know that

`f(-1) = 11/4`
`f(2)=176`

If `f` is linear, then it is of the form

`f(x) =ax+b`

`:. {(-a+b = 11/4),(2a+b = 176) :}`

Solving the system of equations yields

`a = 231/4 and b = 121/2`

If `f` is an exponential function, it is of the form

`f(x) = c*d^x`

`:. {(c/d = 11/4),(cd^2 = 176) :}`

`c=11 and d=4`

If `f` is a power function, it is of the form

`f(x) = alphax^beta`

`:. {(alpha(-1)^beta=11/4),(alpha2^beta = 176) :}`

By assuming `beta` to be an integer,

`alpha = 11/4 and beta =6`