Question

Evaluate the function h(x)=x+ + x2 +1 at the given values of the independent variable and simplify. a. h(2) b. h(-1) c. h( - ) d. h(3a) a. h(2)=L(Simplify your answer.)

Answer 1

Solution-

We have given the function as

  ....(1)

f(1) = x+ + x2 +1

Now, let find the value of f(x) for different values of x.

(a) For f(2)

Putting x =2 in equation (1), we get

$f(2)=(2)^4+(2)^2+1$

On simplifying it,we get

$f(2)=16+4+1$

Or

f(2) = 21

Hence, f(2) = 21

(b) For f(-1)

Putting x = -1 in equation (1), we get

$f(-1)=(-1)^4+(-1)^2+1$

On simplifying it,we get

$f(-1)=1+1+1$

Or

$f(-1)=3$

Hence, f(-1) = 3

(c) For f(- x)

On replacing x by -x in equation (1), we get

$f(-x)=(-x)^4+(-x)^2+1$

On simplifying it,we get

$f(-x)=x^4+x^2+1$

Hence,

$f(-x)=f(x)=x^4+x^2+1$

(d) For f(3a)

On replacing x by 3a in equation (1), we get

$f(3a)=(3a)^4+(3a)^2+1$

On simplifying it,we get

$f(3a)=(3)^4a^4+(3)^2a^2+1$

Or

$f(3a)=81a^4+9a^2+1$

Hence,

$f(3a)=81a^4+9a^2+1$