f (x) = x* +8x+15 g (x) = x +5 find ({ •g) (x) x3 +68x2 +75 or x +13x2 +55x+ 75 or x3 +23x2 +45x+ 75 or x +13x2 +55x 55x+20

To find \((f \circ g)(x)\), we need to substitute \(g(x)\) into \(f(x)\). ### Given functions: - \( f(x) = x^3 + 8x + 15 \) - \( g(x) = x + 5 \) ### Finding \( (f \circ g)(x) \): 1. Compute \( g(x) \): \[ g(x) = x + 5 \] 2. Substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(x + 5) \] 3. Now, replace \( x \) in \( f(x) \) with \( x + 5 \): \[ f(x + 5) = (x + 5)^3 + 8(x + 5) + 15 \] 4. Calculate \( (x + 5)^3 \): \[ (x + 5)^3 = x^3 + 3 \cdot 5 x^2 + 3 \cdot 5^2 x + 5^3 \] \[ = x^3 + 15x^2 + 75x + 125 \] 5. Now substitute this back: \[ f(x + 5) = [x^3 + 15x^2 + 75x + 125] + 8(x + 5) + 15 \] \[ = x^3 + 15x^2 + 75x + 125 + 8x + 40 + 15 \] \[ = x^3 + 15x^2 + (75x + 8x) + (125 + 40 + 15) \] \[ = x^3 + 15x^2 + 83x + 180 \] ### Result: So, \((f \circ g)(x) = x^3 + 15x^2 + 83x + 180\). This expression does not appear to match any of the options you provided. Please check the functions or options again to ensure accuracy.