Mathematics equation in substitution method

History

• • Today
  • Let $f(x)=\frac{3}{4} x+10$, $g(x)=x^{2}-3$. What is the value of $f(-2-g(3))$ ?
    

Supports:
G











To find the value of
f(−2−g(3)) f(-2 - g(3)) f(−2−g(3))
, we will follow these steps: 1. Calculate
g(3) g(3) g(3)
. 2. Substitute
g(3) g(3) g(3)
into the expression
−2−g(3) -2 - g(3) −2−g(3)
. 3. Calculate
f(−2−g(3)) f(-2 - g(3)) f(−2−g(3))
. Step 1: Calculate
g(3)\mathbf{ g(3) }g(3)
The function
g(x) g(x) g(x)
is defined as:
g(x)=x2−3 g(x) = x^2 - 3 g(x)=x2−3
Substituting
x=3 x = 3 x=3
:
g(3)=32−3=9−3=6 g(3) = 3^2 - 3 = 9 - 3 = 6 g(3)=32−3=9−3=6
Step 2: Substitute
g(3)\mathbf{ g(3) }g(3)
into
−2−g(3)\mathbf{ -2 - g(3) }−2−g(3)
Now we substitute
g(3)=6 g(3) = 6 g(3)=6
:
−2−g(3)=−2−6=−8 -2 - g(3) = -2 - 6 = -8 −2−g(3)=−2−6=−8
Step 3: Calculate
f(−8)\mathbf{ f(-8) }f(−8)
The function
f(x) f(x) f(x)
is defined as:
f(x)=34x+10 f(x) = \frac{3}{4} x + 10 f(x)=43x+10
Substituting
x=−8 x = -8 x=−8
:
f(−8)=34(−8)+10 f(-8) = \frac{3}{4}(-8) + 10 f(−8)=43(−8)+10
Calculating
34(−8) \frac{3}{4}(-8) 43(−8)
:
34(−8)=−6 \frac{3}{4}(-8) = -6 43(−8)=−6
Now, substituting back into
f(−8) f(-8) f(−8)
:
f(−8)=−6+10=4 f(-8) = -6 + 10 = 4 f(−8)=−6+10=4
Thus, the value of
f(−2−g(3)) f(-2 - g(3)) f(−2−g(3))
is:
4 \boxed{4} 4