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If #f(x)=4x^2-24x+36#, how do you find the value f(x)=4?

Answer 1

Genesis Allen

To find the value of ( f(x) ) when ( f(x) = 4 ), set the given function equal to 4 and solve for ( x ):

[ 4x^2 - 24x + 36 = 4 ]

[ 4x^2 - 24x + 36 - 4 = 0 ]

[ 4x^2 - 24x + 32 = 0 ]

Now, solve the quadratic equation using methods like factoring, completing the square, or the quadratic formula.

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Answer 2

Ethan Adkins

You know that your function looks like this

#f(x) = 4x^2 - 24x + 36#

If #f(x) = 4#, then you can say that

#f(x) = 4x^2 - 24x + 36 = 4#

Get this equation in quadratic form by adding #-4# to both sides of the equation

#4x^2 - 24x + 36 - 4= color(red)(cancel(color(black)(4))) - color(red)(cancel(color(black)(4)))#

#4x^2 - 24x + 32 = 0#

This is equivalent ot

#4(x^2 - 6x + 8) = 0#

You can use the quadratic formula to get the two solutions for this equation

#x_(1,2) = (-(-6) +- sqrt((-6)^2 - 4 * 1 * 8))/2#

#x_(1,2) = (6 +- sqrt(36 - 32))/2#

#x_(1,2) = (6 +- 2)/2 = {(x_1 = 4), (x_2 = 2) :}#

This means that you have two values of #x# for which #f(x)# is equal to #4#.

#f(2) = 4# and #f(4) = 4#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.