Given f, left bracket, x, right bracket, equals, 3, x, squared, plus, 2f(x)=3x
2
+2, find f, left bracket, minus, 7, right bracketf(−7)
To find f(−7), we need to substitute x = -7 into the given equation:
f(x) = 3x^2 + 2f(x) = 3x + 2
Substituting x = -7:
f(-7) = 3(-7)^2 + 2f(-7)
Now we need to simplify the equation by solving for f(-7).
To find f(-7), we need to substitute -7 into the given equation for x and solve for f(x):
f(x) = 3x^2 + 2f(x)/3x + 2
Substituting -7 for x:
f(-7) = 3(-7)^2 + 2f(-7)/(3*(-7)) + 2
Simplifying:
f(-7) = 147 + 2f(-7)/(-21) + 2
Now let's solve for f(-7). We'll start by isolating the term 2f(-7)/(-21):
f(-7) + 2f(-7)/(-21) = 147 + 2
Combining the fractions on the left side:
(-21f(-7) + 2f(-7))/(-21) = 147 + 2
Now multiply both sides by -21 to eliminate the denominator on the left:
-21f(-7) + 2f(-7) = (-21)(147 + 2)
Simplifying:
-21f(-7) + 2f(-7) = -3087 - 42
Combine like terms:
-19f(-7) = -3129
Now divide both sides by -19 to solve for f(-7):
f(-7) = (-3129)/(-19)
Simplifying:
f(-7) = 165
To find f(-7), we substitute -7 for x in the equation f(x) = 3x^2 + 2f(x) = 3x^2 + 2.
1. Start with the equation: f(x) = 3x^2 + 2.
2. Replace x with -7: f(-7) = 3(-7)^2 + 2.
3. Simplify the equation: f(-7) = 3(49) + 2.
4. Calculate the results: f(-7) = 147 + 2.
5. Add the numbers: f(-7) = 149.
Therefore, f(-7) = 149.