Answer :
To find the value of [tex]\( c \)[/tex] given the function [tex]\( f(x) = x^2 - 15 \)[/tex] and that [tex]\( f(c) = 49 \)[/tex], follow these steps:
1. Substitute the value of [tex]\( f(c) \)[/tex] into the function:
We know that [tex]\( f(c) = 49 \)[/tex]. This means that when [tex]\( x = c \)[/tex], the function value is 49. So, we set up the equation:
[tex]\[
c^2 - 15 = 49
\][/tex]
2. Solve the equation for [tex]\( c \)[/tex]:
To solve for [tex]\( c \)[/tex], start by adding 15 to both sides of the equation to isolate the [tex]\( c^2 \)[/tex] term:
[tex]\[
c^2 = 49 + 15
\][/tex]
[tex]\[
c^2 = 64
\][/tex]
3. Find the square roots:
To find [tex]\( c \)[/tex], take the square root of both sides of the equation. Remember that there are two possible square roots (positive and negative):
[tex]\[
c = \pm \sqrt{64}
\][/tex]
[tex]\[
c = \pm 8
\][/tex]
4. Conclusion:
The possible values for [tex]\( c \)[/tex] are [tex]\( c = 8 \)[/tex] and [tex]\( c = -8 \)[/tex].
1. Substitute the value of [tex]\( f(c) \)[/tex] into the function:
We know that [tex]\( f(c) = 49 \)[/tex]. This means that when [tex]\( x = c \)[/tex], the function value is 49. So, we set up the equation:
[tex]\[
c^2 - 15 = 49
\][/tex]
2. Solve the equation for [tex]\( c \)[/tex]:
To solve for [tex]\( c \)[/tex], start by adding 15 to both sides of the equation to isolate the [tex]\( c^2 \)[/tex] term:
[tex]\[
c^2 = 49 + 15
\][/tex]
[tex]\[
c^2 = 64
\][/tex]
3. Find the square roots:
To find [tex]\( c \)[/tex], take the square root of both sides of the equation. Remember that there are two possible square roots (positive and negative):
[tex]\[
c = \pm \sqrt{64}
\][/tex]
[tex]\[
c = \pm 8
\][/tex]
4. Conclusion:
The possible values for [tex]\( c \)[/tex] are [tex]\( c = 8 \)[/tex] and [tex]\( c = -8 \)[/tex].
