The function f : R $\to$ R defined by f (x) = 2^x + 2^(|x|) is

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(d) many-one and into Graph for the given function is as follows. A line parallel to X axis is cutting the graph at two different values. Therefore, for two different values of x we are getting the same value of y. That means it is many one function.[2 , $\infty$ ) and R is the co-domain of the given function. Hence, Co-domain $\neq$ Range Therefore, the given function is into. [Solution diagram: 41545_solution_1.png]

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