Question

if f(x)=2x^3-6x+4x-5 and g(x)=3x^2-9, then the value of f(1)+g(-2) is

Answer 1

Given :-

$\sf f ( x ) = 2x³ - 6x + 4x - 5$ and $\sf g(x) = 3x² - 9$

To Find :-

The value of $\sf f ( 1 ) + g(-2)$

Solution :-

Let's start with $\sf f ( x )$ ;

$\quad \leadsto \quad \sf f ( x ) = 2x³ - 6x + 4x - 5$

Can be further written as ;

${ : \implies \quad \sf f(x) = 2x³-2x-5}$

Now , At x = 1 ;

${ : \implies \quad \sf f(1) = 2 \times ( 1 )³ - 2 \times 1 - 5 }$

${ : \implies \quad \sf f(1) = 2 \times 1 - 2 - 5 }$

${ : \implies \quad \sf f(1)= \cancel{2} - \cancel{2} - 5 }$

${ : \implies \quad \sf f(1)= - 5 \quad \qquad \bf ---(i)}$

Now , consider ;

$\quad \leadsto \quad \sf g(x) = 3x² - 9$

Now , At x = - 2 ;

${ : \implies \quad \sf g(-2) = 3 \times ( - 2 )² - 9 }$

${ : \implies \quad \sf g(-2) = 3 \times 4 -9}$

${ : \implies \quad \sf g(-2) = 12 - 9 }$

${ : \implies \quad \sf g(-2) = 3 \quad \qquad \bf ---(ii)}$

Adding $\bf (i)$ and $\bf (ii)$ ;

$\quad \leadsto \quad \sf f ( 1 ) + g(-2)$

${ : \implies \quad \sf f ( 1 ) + g(-2)= - 5 + 3 }$

${ : \implies \quad \bf f ( 1 ) + g(-2)= - 2}$

Henceforth , The Required Answer is - 2 :)