4.3.1 Let f be the the function given by f(z) = 2x + 1 . Calculate f-1(1) 4.3.2

Question

4.3.1 Let f be the the function given by f(z) = 2x + 1 . Calculate f-1(1) 4.3.2 Let f be the the function whose graph is a line with slope 3. The graph of the inverse function f-1 is also a line. What is the slope of this line? 4.3.3 Let f be the the function given by f(x) = 1+2 Calculate f about this? What are the domains and ranges of f and f- What do you notice 4.3.4 Let f be the the function given by f(z) = (1-1). 1 Calculate f-1(x) 4.3.5 Find a domain consisting of exactly three disjoint intervals so that the function given by f(x) s invertible on this domain, the domain of the inverse function is [0, oo), and the range of the inverse function contains at least one negative number and one positive number. Sketch the graph both f and f-1

Explanation / Answer

1) f(x) = 2x +1

y = 2x + 1

switching x and y

x = 2y + 1

solving for y

x - 1 = 2y

y = ( x-1 ) / 2

f^-1 (x) = (x-1) /2

2) slope of function f is 3

then slopes of inverse function are multiplicaton inverse of each other

hence, slope of inverse function would be 1/3

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