Find a possible formula?

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Answer 1 · 2018-06-27T20:36:42

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

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

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

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,

$alpha = 11/4 and beta =6$