Composite functions and notation. Let ?f? (x)?=x -4, ?g? (x)=x and ?F(x)=1? /(x-3). Simplify or evaluate the following expressions. f(2+h)?f(2) h

Step by step solution Step 1 of 1 2 3 Consider three different functions f(x)=x -4 (x)=x and F(x)= 1/(x-3). f(2+h)f(2) For evaluating the value of h first find the values of f(2+h)and f(2). If we want to find the values of fu nction (x)for =2+h and x =2 we must use these values in the relation for the f unction (x).This is very easy, just follow the next steps: 2 f(x) = x 4 2 f(2+h) = (2+h) 4 f(2) = 2 4 = 44 = 0 f(2+h)f(2) Now we use the values for f(2+h)and f(2)in order to calculate h : f(2+h)f(2) (2+h) 40 h = h (2+h) 4 = h 2 2 2 Based on the relation (a+b) = a +2ab+b we can write the following: 2 f(2+h)f(2)= (2+h) 4 h h = 2 +2·2h+h 4 h = 4+4h+h 4 2 = 4h+h h = h(h+4) h = 4+h f(2+h)f(2) So the final value of function h is +4.