Question

if f(x)= x² and g(x)=|x|, find the following functions, i) f+g ii) f-g iii) fg iv) 2f v) f^2 vi)f+3​

Answer 1

Answer:

(i)f(x)+ g(x) = ${x^2 + x (x < 0)\\, x^2 - x (x > 0 )}$

(ii) f(x) - g(x) = ${x^2 - x (x > 0)\\, x^2 + x (x < 0 )}$

(iii) f(x)g(x) = $-x^3 , x^3$

(iv)2f(x) =  2$x^2$

(v)$f^2(x)$ = $x^4$

(vi) f(x) + 3 = $x^2 + 3$

Step-by-step explanation:

Explanation:

Given, f(x) = $x^2$ and g(x) = |x|

So,  with the help of given information, we need to find the values of, i) f+g ii) f-g iii) fg iv) 2f v) f^2 vi)f+3​.

Step 1:

From the question we have  f(x) = $x^2$ and g(x) = |x|

So , f(x)+ g(x) = $x^2 + |x|$

⇒ f(x) + g(x) ={ ${x^2 + x (x < 0)\\, x^2 - x (x > 0 )}$}

Value of  f(x) - g(x) = ${x^2 - x (x > 0)\\, x^2 + x (x < 0 )}$

Value of  f(x)g(x)  =  ${x^2 (-x) (x > 0)\\, x^2 (+x) (x < 0 )}$

⇒ f(x)g(x) = $-x^3 , x^3$

Value of 2f(x) = 2 × $x^2$ = 2$x^2$ .

Value of $f^2(x)$ = $(x^2)^2$ = $x^4$

Value of f(x) + 3 = $x^2 + 3$ .

Final answer:

Hence , the value of f(x)+ g(x) = ${x^2 + x (x < 0)\\, x^2 - x (x > 0 )}$,

f(x) - g(x) = ${x^2 - x (x > 0)\\, x^2 + x (x < 0 )}$ , f(x)g(x) = $-x^3 , x^3$  ,2f(x) =  2$x^2$  ,

$f^2(x)$ = $x^4$  and f(x) + 3 = $x^2 + 3$  .

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Answer 2

Answer:

Hence , the value of f(x)+ g(x) =  ( x² +x( x<0) ),  ( x²-x( x<0) )

f(x) - g(x) =  ( x²-x( x<0) ), ( x² +x( x<0) )

f(x)g(x) = -x³ , x³

2f(x) = 2x²

f² (x) = x⁴

f(x) + 3 = x²+3

Step-by-step explanation:

Given, f(x) = x²  and g(x) = |x|

So,  with the help of this values , we have to find the values of, i) f+g ii) f-g iii) fg iv) 2f v) f^2 vi)f+3​.

f(x) = x²  and g(x) = |x|

So , f(x)+ g(x) = x² +|x|

f(x) + g(x) = ( x² +x( x<0) ),  ( x²-x( x<0) )

Value of  f(x) - g(x) =  ( x²-x( x<0) ), ( x² +x( x<0) )

Value of  f(x)g(x)  =  x²(-x) ( x>0) , x²(+x)  ( x<0)

f(x)g(x) = -x³ , x³

Value of 2f(x) = 2 x x² =2x²

Value of  f² (x) = (x²)² =x⁴

Value of f(x) + 3 = x²+3

The answer:

Hence , the value of f(x)+ g(x) =  ( x² +x( x<0) ),  ( x²-x( x<0) )

f(x) - g(x) =  ( x²-x( x<0) ), ( x² +x( x<0) )

f(x)g(x) = -x³ , x³

2f(x) = 2x²

f² (x) = x⁴

f(x) + 3 = x²+3

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