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Home » Find the values of x for which the functions f (x) = 3×2 – 1 and g (x) = 3 + x are equal
Find the values of x for which the functions f (x) = 3×2 – 1 and g (x) = 3 + x are equal
CBSE | Class 11 | Maths | NCERT Exemplar | Relations and Functions
Find the values of x for which the functions f (x) = 3×2 – 1 and g (x) = 3 + x are equal

Solution:

Provided,

f and g functions defined by f (x) = {3x}^{2} {-} 1 and g (x) = 3 + x

For what real numbers x, f (x) = g (x)

In order to satisfy the condition f(x) = g(x),

We also need to satisfy

3^{2}-1=3+x

\Rightarrow 3^{2}-x-3-1=0

\Rightarrow 3^{2}-x-4=0

When we split the middle term,

We have,

\Rightarrow 3^{2}+3 x-4 x-4=0

\Rightarrow 3x(x+1)-4(x+1)=0

\Rightarrow(3 x-4)(x+1)=0

\Rightarrow 3 x-4=0 \text { or } x+1=0

\Rightarrow 3 x=4 \text { or } x=-1

\Rightarrow x=4 / 3,-1

As a result, for x=4 / 3,-1, f(x)=g(x), that means the given functions are equal.

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