Find the kernel and range of the following lincar operators on P3: (a) L(p(x)) = p(x) - xp'(x) (b) L(p(x)) = p(0)x + p(1)
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- If f is invertible and f(4) = 14, then f(14) = -1 and (f(4))For #'s 11-14 , h(x) = (f og)(x) Let h(x) = (2x–5) and f(x)=x', find g(x) Let h(x) = Vx-5 and f(x)= Vx, find g(x) Let h(x)= (5x + 1) -(5x +1) and S(x) = x² – x, find g(x) 11. 12. 13. 14. Let h(x) = V(-3x – 2) and f(x) = vx, find g(x)Suppose that the functions s and t are defined for all real numbers x as follows. s (x)%3x-5 t (x) =3x+3 Write the expressions for (s-t)(x) and (s t)(x) and evaluate (s+t)(4). (+-)(+) = [0 %3D (s-t)(x) = [ %3D (s+t)(4) = [ %D
- Suppose that the functions h and g are defined as follows. h (x)= (3 +x)(-4+x) g (x) =1-7x (a) Find (2). h (b) Find all values that are NOT in the domain of –. g If there is more than one value, separate them with commas. (2) = 0 (a) %3D (b) Value(s) that are NOT in the domain of oloSuppose that the functions s and t are defined for all real numbers x as follows. s (x) = I (x) =2x² x+1 Write the expressions for (t+s) (x) and (t-s) (x) and evaluate (t's) (2). (1+ s)(x) = 0 %3D (1 - s)(x) = 0 (1-s)(2) = ]That f(x) = -2x, g(x)= |x + 4|, and h(x)2/x-3. Evalute the functions for the given values of x: a)(g º f)(x) b)(g º f º h)(3) c)f(7)
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