Given f, left bracket, x, right bracket, equals, 3, x, squared, plus, 2f(x)=3x

Question

2
+2, find f, left bracket, minus, 7, right bracketf(−7)

Answer 1

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