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

if t ≠ 5

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

To find: , if t ≠ 5

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 = 5 in above function, we get

f (5) = (5)² + 7 = 25 + 7 = 32……..(ii)

We need to find,

Substituting values from equation (i) and (ii), we get

But we know a²-b² = (a + b)(a-b), so above equation becomes,

Cancelling the like terms, we get