Question

Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).

y+3x^2=5
f(x)=?
f(2)=?

Answer 1

• 
  `f(2) = - 7`
• 
  `f(x) = 5 - 3x^2`

Explanation:

To find:-

• The value of
  `f(2)`

Answer:-

We are here a given a equation, with some steps to follow, in order to find out the value of
`f(2)`.

Step 1 :- Solve the equation in terms of y ,

The given equation to us is,

`\longrightarrow y + 3x^2 = 5\\`

To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .

`\longrightarrow y = 5 - 3x^2 \\`

Step 2 :- Replace y with function notation
`f(x)`

Just simply replace y here with f(x) as ,

`\longrightarrow f(x) = 5 - 3x^2\\`

Step 3 :- Find f(2) .

To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,

`\longrightarrow f(2) = 5 - 3(2)^2\\`

Simplify,

`\longrightarrow f(2) = 5 - 3(4)\\`

`\longrightarrow f(2) = 5 - 12\\`

`\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\`

Hence the required answer is -7 .

Answer 2

`f(x)=-3x^2+5`

`f(2) = -7`

Explanation:

Given equation:

`y+3x^2=5`

To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:

`\implies y+3x^2-3x^2=5-3x^2`

`\implies y=-3x^2+5`

Replace y with the function notation f(x):

`f(x)=-3x^2+5`

Finally, to find the value of f(2), substitute x = 2 into the function:

`\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}`