Evaluate the following function at the values t 4 and t h

Evaluate the following function at the values t + 4 and t + h. and find g(t + h) - g(t)/h g(t) = 2t^3 - 9t g(t + 4) = (Simplify your answer. Type an expression using t as the variable. Use integers or fractions for any numbers in the expression.) g(t + h) = (Simplify your answer. Use integers or fractions for any numbers in the expression.) g(t + h)-g(t)/h = (Simplify your answer Use integers or fractions for any numbers in the expression) Use the given graph of y =f(x) to answer the following questions. What is the domain of f^-1? What is the range of f^-1? What is the y-intercept of f^-1? Evaluate f^-1 (0). Evaluate f^-1 (- 2). Evaluate f^-1 (6). Evaluate f^-1 (1). The domain of f^-1 is. (Type your answer in interval notation.) The range of f^-1 is. (Type your answer in interval notation.) The y-intercept of f^-1 is. (Type an integer or a decimal.) f^-1(0)= f^-1(-2)= f^-1(6)= f^-1(1)=

Solution

1) given g(t)=2t³-9t

g(t+4)=2(t+4)³-9(t+4)

g(t+4)=2(t³+12t²+48t+64)-9t-36

g(t+4)=2t³+24t²+96t+128-9t-36

g(t+4)=2t³+24t²+87t+92

g(t+h)=2(t+h)³-9(t+h)

g(t+h)=2(t³+3t²h+3th²+h³)-9t-9h

g(t+h)=2t³+6t²h+6th²+2h³-9t-9h

[g(t+h)-g(t)]_/h =[2t³+6t²h+6th²+2h³-9t-9h -2t³-24t²-87t-92]_/h

[g(t+h)-g(t)]_/h =[6t²h+6th²+2h³-9h -24t²-78t-92]_/h

[g(t+h)-g(t)]_/h =[6t²+6th+2h²-9 -24(t²_/h)-78(t_/h)-(92_/h)

2)a)domain of f^-1 is [-2,6]

b)range of f^-1 is [-3,4]

c)y intercept of f ^-1is -2

d)f^-1(0)=-2

e)f^-1(-2)=-3

f)f^-1(6)=4

g)f^-1(1)=0