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Home » If f and g are real functions defined by f (x) = x2 + 7 and g (x) = 3x + 5, find each of the following (a) f (– 2) + g (– 1) (b) f (t) – f (– 2)
If f and g are real functions defined by f (x) = x2 + 7 and g (x) = 3x + 5, find each of the following (a) f (– 2) + g (– 1) (b) f (t) – f (– 2)
CBSE | Class 11 | Maths | NCERT Exemplar | Relations and Functions
If f and g are real functions defined by f (x) = x2 + 7 and g (x) = 3x + 5, find each of the following (a) f (– 2) + g (– 1) (b) f (t) – f (– 2)

Solution:

Provided,

f and g are real functions such that f(x)=x^{2}+7 and g(x)=3 x+5

(a) f(-2)+g(-1)

f(x)=x^{2}+7

Substitute x = {-}2 in f(x), we have

f(-2)=(-2)^{2}+7=4+7=11 \ldots \ldots \dots (i)

And,

g (x) = 3x + 5

Substitute x = {-}1 in g(x), we have

g(-1)=3(-1)+5

=-3+5=2 \ldots \ldots \dots (ii)

Now add eq.(i) and eq.(ii),

We have,

f(-2)+g(-1)=11+2=13

(b) f(t)-f(-2)

f(x)=x^{2}+7

Substitute x = t in f(x), we have

f(t)=t^{2}+7 \ldots \ldots \dots (i)

Now, consider the same function,

f (x) = x^{2} + 7

Substitute x = {-}2 in f(x), we have

f(-2)=(-2)^{2}+7=4+7=11 \ldots \ldots \dots (ii)

Now, subtract eq.(i) with eq.(ii),

We have,

f(t)-f(-2)=t^{2}+7-11=t^{2}-4

i

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