If f and g are real functions defined by f (x) = x² + 7 and g (x) = 3x + 5, find each of the following
f (t) – f (– 2)

Question

If f and g are real functions defined by f (x) = x2 + 7 and g (x) = 3x + 5, find each of the followingf (t) – f (– 2)

Philoid · Accepted Answer

Given: f and g are real functions such that f (x) = x² + 7 and g (x) = 3x + 5

To find: f (t) – f (– 2)

Explanation: the given

f (x) = x² + 7

Now putting x = t in above function, we get

f (t) = t² + 7……..(i)

and again, considering the same function

f (x) = x² + 7

Now putting x = -2 in above function, we get

f (-2) = (-2)² + 7 = 4 + 7 = 11…….(ii)

Subtracting equation (i) with (ii), we get

f (t) – f (– 2) = t² + 7-11

= t²-4